Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

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dc.creatorConnell, Patrick
dc.creatorFrolov, Valeri P.
dc.creatorKubiznak, David
dc.date2008-03-23
dc.date.accessioned2026-07-07T11:49:18Z
dc.date.available2026-07-07T11:49:18Z
dc.descriptionWe obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces are independently parallel-propagated. This allows one to reduce the parallel transport equations to a set of the first order ordinary differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equations of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three, four, and five dimensional Kerr-NUT-(A)dS are considered and it is shown that the obtained first order equations can be solved by a separation of variables.
dc.description14 pages, no figures
dc.identifierhttps://arxiv.org/abs/0803.3259
dc.identifierhttp://arxiv.org/abs/0803.3259
dc.identifierPhys.Rev.D78:024042,2008
dc.identifierdoi:10.1103/PhysRevD.78.024042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/203183
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleSolving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes
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